Nanopores attracted a great deal of scientific interest as templates for
biological sensors as well as model systems to understand transport phenomena
at the nanoscale. The experimental and theoretical analysis of nanopores has
been so far focused on understanding the effect of the pore opening diameter on
ionic transport. In this article we present systematic studies on the
dependence of ion transport properties on the pore length. Particular attention
was given to the effect of ion current rectification exhibited for conically
shaped nanopores with homogeneous surface charges. We found that reducing the
length of conically shaped nanopores significantly lowered their ability to
rectify ion current. However, rectification properties of short pores can be
enhanced by tailoring the surface charge and the shape of the narrow opening.
Furthermore we analyze the relationship of the rectification behavior and ion
selectivity for different pore lengths. All simulations were performed using
MsSimPore, a software package for solving the Poisson-Nernst-Planck (PNP)
equations. It is based on a novel finite element solver and allows for
simulations up to surface charge densities of -2 e/nm^2. MsSimPore is based on
1D reduction of the PNP model, but allows for a direct treatment of the pore
with bulk electrolyte reservoirs, a feature which was previously used in higher
dimensional models only. MsSimPore includes these reservoirs in the
calculations; a property especially important for short pores, where the ionic
concentrations and the electric potential vary strongly inside the pore as well
as in the regions next to pore entrance
